Black brane solutions governed by fluxbrane polynomials

A family of composite black brane solutions in the model with scalar fields and fields of forms is presented. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat “internal” spaces. The solutions are governed by moduli functions Hs (s=1,…,m) obeying non-linear differential equations with certain boundary conditions imposed. These master equations are equivalent to Toda-like equations and depend upon the non-degenerate (m×m) matrix A. It was conjectured earlier that the functions Hs should be polynomials if A is a Cartan matrix for some semisimple finite-dimensional Lie algebra (of rank m). It is shown that the solutions to master equations may be found by using so-called fluxbrane polynomials which can be calculated (in principle) for any semisimple finite-dimensional Lie algebra. Examples of dilatonic charged black hole (0-brane) solutions related to Lie algebras A1, A2, C2 and G2 are considered.